Final answer:
To find the moment of inertia about an axis passing through one of the corners of an equilateral triangle, perpendicular to the triangle's plane, we can use the parallel axis theorem. The moment of inertia about the center of mass of the triangle is (M L²)/12, where M is the mass of each point mass and L is the length of the side of the triangle.
Step-by-step explanation:
To find the moment of inertia about the axis passing through one of the corners of an equilateral triangle, perpendicular to the plane of the triangle, when three point masses are placed at the corners of the triangle, we can use the parallel axis theorem.
Using the parallel axis theorem, the moment of inertia about the point of rotation is given by I = ICM + Md², where ICM is the moment of inertia about the center of mass, M is the total mass, and d is the perpendicular distance between the axis of rotation and the center of mass.
For an equilateral triangle, the moment of inertia about the center of mass is given by ICM = (M L²)/12, where M is the mass of each point mass and L is the length of the side of the equilateral triangle.